Quantum computing promises fast solutions to a wide range of optimization problems and thus holds considerable potential for machine learning [1]-[3]. However, while the quantum machine learning literature so far mainly focused on the quantum gate paradigm, noticeable technological progress leading to commercial devices is happening in adiabatic quantum computing [4], [5]. Current adiabatic quantum computers are geared towards solving quadratic unconstrained binary optimization problems or Ising models. A simple strategy for setting up established learning algorithms to run on such devices is therefore to attempt to (re-)formulate or approximate their minimization or maximization objectives in terms of Ising models. In this paper, we apply this strategy to a simple unsupervised learning problem, namely binary clustering.

In this blog, we will discuss about clustering of customer activities for 24 hours by using K-means clustering feature in Tableau 10. This type of clustering helps you create statistically-based segments that provide insights about similarities in different groups and performance of the groups when compared to each other. You can use clustering on any type of visualization ranging from scatter plots to text tables and even maps. In our previous blog post – "Call Detail Record Analysis – K-means Clustering with R", we have discussed about CDR analysis using unsupervised K-means clustering algorithm. A daily activity file from Dandelion API is used as a data source, where the file contains CDR records generated by the Telecom Italia cellular network over the city of Milano.

The following simpler spectral partitioning approach (thresholding on the second dominant eigenvector) can also be applied for automatic separation of the foreground from the background.

Clustering is the grouping of objects together so that objects belonging in the same group (cluster) are more similar to each other than those in other groups (clusters). In this intro cluster analysis tutorial, we'll check out a few algorithms in Python so you can get a basic understanding of the fundamentals of clustering on a real dataset. For the clustering problem, we will use the famous Zachary's Karate Club dataset. The story behind the data set is quite simple: There was a Karate Club that had an administrator "John A" and an instructor "Mr. Then a conflict arose between them, causing the students (Nodes) to split into two groups.

The learning of mixture models can be viewed as a clustering problem. Indeed, given data samples independently generated from a mixture of distributions, we often would like to find the correct target clustering of the samples according to which component distribution they were generated from. For a clustering problem, practitioners often choose to use the simple k-means algorithm. k-means attempts to find an optimal clustering which minimizes the sum-of-squared distance between each point and its cluster center. In this paper, we provide sufficient conditions for the closeness of any optimal clustering and the correct target clustering assuming that the data samples are generated from a mixture of log-concave distributions. Moreover, we show that under similar or even weaker conditions on the mixture model, any optimal clustering for the samples with reduced dimensionality is also close to the correct target clustering. These results provide intuition for the informativeness of k-means (with and without dimensionality reduction) as an algorithm for learning mixture models. We verify the correctness of our theorems using numerical experiments and demonstrate using datasets with reduced dimensionality significant speed ups for the time required to perform clustering.

Spectral clustering is a widely studied problem, yet its complexity is prohibitive for dynamic graphs of even modest size. We claim that it is possible to reuse information of past cluster assignments to expedite computation. Our approach builds on a recent idea of sidestepping the main bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by using fast Chebyshev graph filtering of random signals. We show that the proposed algorithm achieves clustering assignments with quality approximating that of spectral clustering and that it can yield significant complexity benefits when the graph dynamics are appropriately bounded.

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experiment results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.

Density-based clustering is a technique that allows to partition data into groups with similar characteristics (clusters) but does not require specifying the number of those groups in advance. In density-based clustering, clusters are defined as dense regions of data points separated by low-density regions. Density is measured by the number of data points within some radius. There are different methods of density-based clustering. The most popular are DBSCAN (density-based spatial clustering of applications with noise), which assumes constant density of clusters, OPTICS (ordering points to identify the clustering structure), which allows for varying density, and "mean-shift".

TL;DR Abstract - I built ZombieWriter, a Ruby gem that will enable users to generate news articles by aggregating paragraphs from other sources. It can use either machine learning algorithms (Latent Semantic Analysis and k-means clustering) or randomization to generate human-readable articles. In this article, I demonstrate how ZombieWrtier can use machine learning to create a Markdown file containing 17 human-readable articles. After finishing the demonstration and comparing the output to a randomization process, I then explain possible "future research" plans to improve the text generation process. I am not yet ready to claim that this technology is disruptive. Machine learning is hot (to put it mildly). The paradigm of using data instead of code to program machines has been applied to solve a variety of real-world problems.

Density-based clustering is a technique that allows to partition data into groups with similar characteristics (clusters) but does not require specifying the number of those groups in advance. In density-based clustering, clusters are defined as dense regions of data points separated by low-density regions. Density is measured by the number of data points within some radius. There are different methods of density-based clustering. The most popular are DBSCAN (density-based spatial clustering of applications with noise), which assumes constant density of clusters, OPTICS (ordering points to identify the clustering structure), which allows for varying density, and "mean-shift".